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Cutoff profile of the colored ASEP: GOE Tracy-WidomProbability
|Speaker:||Lingfu Zhang, UC Berkeley|
|Start time:||Wed, Jan 25 2023, 10:00AM|
The colored Asymmetric Simple Exclusion Process (ASEP) in a finite interval (also referred to as the biased card shuffling or the random Metropolis scan) is a well-studied Markov chain, since Diaconis-Ram, 2000. A few years ago, a total-variation cutoff was proved for this chain using hydrodynamic techniques (Labbé-Lacoin, 2016). In this talk, I will explain how to obtain more precise information on the cutoff, in particular, to establish the conjectured GOE Tracy-Widom cutoff profile. The proof relies on coupling arguments as well as symmetries obtained from Hecke algebra, and uses recent results on the scaling limit of the (uncolored) ASEP as an input. Some related open problems will also be discussed.